Realization of multi-agent topologies facilitates in understanding network characteristics, agents interactions and group dynamics in wide range of engineering applications as well as in pedagogical courses [1]}, [2]}. In network control and dynamics research community, the analysis and synthesis of multi-agent topologies have drawn serious attention over the past [1]}, [4]}, [5]}. Most of the real world network topologies can be represented mathematically by using their corresponding graphs. For instance, in cooperative robotics applications [1]}, a multi-agent system is represented by a graph where nodes are the point-robots and edges are the inter-connections between them. In a decentralized network of multiple agents, the group performance and task accomplishment depend on agents information sharing ability to their neighbors. The connectivity measure of a graph, i.e. the algebraic connectivity, plays vital role in group dynamics as it determines how well the agents can communicate to each other. A connectivity value above zero guarantees that there exists at least one spanning tree [7]} or an information flow path among the members in a group. Earlier research shows a fair amount of contributions [1]}, [9]}, [10]} dedicated to maintaining, controlling and maximizing connectivity of a multi-agent network, during cooperative tasks such as target tracking and formation control [11]}.
